Mathematical ability is essential for almost every aspect of human existence and yet there is large variability in math competency in adults and extremely poor math ability is linked with long-term health problems and higher criminality (Parsons and Bynner, 2005). Math skills at school-entry predict later math achievement and are a better predictor of later overall academic achievement than literacy skills (Jordan, et al., 2009 Duncan et al., 2007). Therefore improving early math skills in very young children could have global effects on academic success and perhaps life outcomes. The goal of this proposal is to build upon a recent finding from our research group demonstrating that training with approximate nonsymbolic arithmetic (ApprA) using dot arrays leads to positive transfer in exact symbolic arithmetic (SymA) performance (Park and Brannon, In press). In Aim 1 we ask why ApprA training improves SymA. We decompose the cognitive ingredients of ApprA training to assess which aspects are critical for improving symbolic arithmetic. In Aim 2 we test specific predictions about how overlap in the brain regions that support approximate nonsymbolic arithmetic and exact symbolic arithmetic give rise to this transfer effect. For example, we ask whether ApprA training changes the neural tuning curves in the intraparietal sulcus, which are known to embody the mental representation of quantity. Such a finding would provide strong evidence that ApprA improves SymA by changing the primitive number sense. Finally Aim 3 proposes an iPad intervention study in a diverse public school district to test the efficacy of ApprA training to improve SymA in young children. Pilot data is presented for all three aims. Understanding the relationship between ApprA and SymA could have broad implications for understanding the roots of human mathematics. While ApprA training is unlikely to be practically useful as an avenue for improving math competency in adults or older children who have mastered the symbolic number system it could be critically important for improving math ability in very young children who have yet to master the symbolic number system.